B737 Captain reported a Fuel Imbalance at top of climb. The flight crew ran the QRH and checklists. After conferring with Operations and Maintenance; the flight crew elected to divert and make a precautionary landing.

Narrative

Shortly after reaching top of climb; #2 engine fuel indicated imbalance of ~900 lbs. lower. Center tank fuel was .61 lbs. remaining and all fuel pumps were on. Completed the QRH; initiated cross feed; contacted Operations Control/Maintenance Control via comms. Observed #2 fuel quantity increase +/- 500 lbs. based on observations we did not suspect fuel leak. FMC annunciations of using reserve fuel; followed by insufficient fuel. Observed #1 engine fuel imbalance. Discussed situation with Operations Control/Maintenance Control and diverted to ZZZ at Dispatch's request. Briefed cabin and passengers. Observed at lower altitude fuel remained balanced but additional FMC messages of insufficient fuel. Observed structural landing weight limit 129.2 lbs. Uneventful landing and termination. Worked with station to disembark passengers into terminal. Communicated with Operations Control and contract maintenance. Contract maintenance was not familiar with aircraft or procedures to diagnose. Maintenance Control was unable to determine the cause of the indication problems and FMC messages. Trip reassigned to reserve crew and departed ~ 11 hours later with a MEL.